1. Field of the Invention
The present invention relates to the use of artificial intelligence and its application to tutorial programs. In particular, a computerized methodology is disclosed for a tutoring curriculum that interacts with the misconceptions of a student.
2. Description of the Related Art
Tutoring relies heavily on the tutor to assume what the student was thinking at the time he or she made a mistake in a problem. Personal tutors assist a student in learning a subject by figuring out that a solution to a problem is wrong and then showing the student a correct solution. However it is often difficult to show the student why he or she is wrong. Understanding why a misconception was made allows the student to acquire a more rational understanding of a problem.
An intelligent tutoring system is defined as an educational program capable of humanlike thought processes, such as reasoning and learning. An application of intelligent tutoring is a computer utilizing educational software derived from expert programming. Expert knowledge in a field is important for programming artificial intelligent systems. Similarly, expert knowledge in a subject, as well as expertise in the teaching of the subject, is necessary for the development of intelligent tutoring systems.
Expert systems and artificial intelligence systems are known in the art. See U.S. Pat. No. 4,670,848 to Schramm. This system is characterized by its interaction with a user in gathering statements through inquiries to develop the most specific understanding possible by matching of the statements with a database. See also, U.S. Pat. No. 5,386,498 to Kakefuda. An expert system is disclosed that expresses knowledge of a human expert using knowledge modules. An inference result is based on a determined certainty factor during execution of the process.
Intelligent tutoring systems utilizing artificial intelligence have also been developed. See, for example, Bloom et al., U.S. Pat. No. 5,597,312 and, in particular, a computer-assisted instruction method taught in xe2x80x9cComputer-Assisted Instruction in Chemistryxe2x80x9d by Lower et al. from the Journal of Chemical Education. 
Intelligent tutoring involves justifying steps by rules as a student works through a problem, ultimately to its solution. An expert can find a correct solution to a problem in the least amount of steps, obviously by having mastered the understanding of the most helpful rules used for the problem. A student learning a subject is best instructed on a step-by-step method because as long as a student gets to a correct solution, even by taking a different xe2x80x98pathxe2x80x99, the student has still been able to rationalize what he or she knows along the way. What the student did not know during the course of the solving of the problem would be rationalized by the system as the student performs each step.
Currently, intelligent tutoring systems rationalize mistakes made by a student by implementing a direct model of misconception, called buggy rules, which are also production rules. A buggy rule anticipates a mistake by a student, so that if the student performs a wrong step in the solution to a problem, the system can target the mistake and take a specific action. This production rule model rationalizes a mistake by matching the student""s mistake to the particular rule violation already anticipated and pre-programmed. The prior art intelligent tutoring system not only figures out that a performed step in a solution is wrong, but also that it is wrong because the student matches the action of the pre-programmed rule. The system then correlates the mistake to this common misconception and suggests to the student that the mistake was made because of the misconception associated with the buggy rule.
Thus, in conventional artificially intelligent tutor systems (ITS) the program is primarily oriented to help the student by showing the right next step and explaining why the right step is right (using the knowledge of the expert system). In the present invention, the rules have a much different outlook inasmuch as they serve to explain to the student why a wrong step is wrong. This is much more important to a beginning student in developing the proper mental schemes than studying or memorizing the correct solution. The prior art can achieve this only when the error is anticipated.
Understanding science and other curriculum means utilizing equations, methods, and rules to ultimately find a solution to a problem. Fundamental rules are sometimes overlooked as a student tries to understand more recently studied subject matter. For instance, a student concentrating solely on a single chapter may overlook or forget a fundamental principle he or she learned prior to the lesson. The student may have also made a simple mistake based on a principle he or she had known before, but simply forgot it or was unaware of its relevance. The student might even have simply made a typographical error, but not realized this has led to an unreasonable result.
Thus, certain mistakes may be made that cannot possibly be matched and correlated to an anticipated buggy rule. The sole use of buggy rules for tutoring students targets only a narrow range of possible mistakes made by a student in a step-by-step method of teaching.
There is a need for a methodology that improves the intelligence of the tutor by implementing a rule set that always allows for a meaningful response and which is used even when the production rules fail. Termed herein as consistency rules, the rules target the mistakes that cannot be explained through application of buggy rules, thereby providing a new way to determine whether a student""s step is xe2x80x9cwrongxe2x80x9d more reliably. This is accomplished by evaluating and comparing the inputted solution to an expanded fundamental rule set representing relevant constraints on the solution to assess whether or not the solution is reasonable.
The conventional assessment of xe2x80x9cwrongxe2x80x9d is that the student""s step is not in the conflict set (the set of all possible correct next steps generated by the expert system). In the present methodology, xe2x80x9cwrongxe2x80x9d is defined as a violation of a consistency rule (CR) in a new tutor rule set. If the set of CR""s is complete for the problem domain, then if a step can be proven to be wrong by a fundamental principle in the context of the student""s work so far, it will violate a CR. Violation of a CR guarantees the step is wrong. A wrong answer not matched or anticipated by a pre-programmed buggy rule can still violate a fundamental principle. The present methodology of using consistency rules allows an educational software program to always say something meaningful when a wrong step in the solution is identified, thereby improving the quality of diagnosis of a student""s mistake.
The present AI methodology is directed to an improved intelligent tutorial utilizing rules that evaluate a constraint on a solution and compare this constraint with an improved, more general rule set. By expanding beyond the model of misconception that accounts for the mistakes of students, in which many student errors were previously unable to be tutored from the sole application of production rules, the consistency rules deliver qualitative, conceptual feedback for intelligent tutors.
This is accomplished by assessing the reasonableness of a solution based on an evaluation of a constraint on the solution imposed by a relevant fundamental principle. The basis of the consistency rule is that any wrong answer had to have violated a relevant principle, even when the error is outside of those normally anticipated by an artificial intelligent system. Thus, the present methodology accounts for all possible violations to provide a meaningful response.
By expanding the fundamental rule set by implementing a means for evaluating a constraint on the solution, the CR""s are further capable of augmenting existing, programmed production rules with the functionalities of the consistency rules. The consistency rules used by the system do not all have to be entirely new. Using existing production rules as consistency rules is helpful. A CR is a more general way of representing expert knowledge than a production rule because it represents a constraint as opposed to a specific step. A production rule is simply a special case of the more general concept of the present implementation of the consistency rule.
A step in the solution to a problem as input by the student is evaluated by the system. In a wrong step, an intelligent tutorial tries to match the mistake made by the student by processing the answer by all buggy rules, pre-programmed by the expert, to determine a possible reason why the student missed the solution. The standard program, then, can judge that the answer is wrong by taking the equivalent steps as the student to come up with the same wrong solution. However, the step made by the student may not match the anticipated buggy rule because the number of wrong answers possible in a problem are not finite. Production rules, or buggy rules, use steps to evaluate the answer. The present methodology is indefinite and does not use steps. Thus, wrong answers that may not be explained by the buggy rule are accounted for. If the solution is outside the range of the constraint, the consistency rule can teach a student a necessary principle relevant to a problem.
In fact, the present methodology allows for more than one response for a single step. A technique is then provided for efficiently diagnosing whether a student has multiple errors in a given single wrong step, and what those errors are.
It is the objective of the present invention to provide a plurality of consistency rules to an intelligent tutor, thereby allowing a wrong step in a solution to a problem, which may not accounted for by buggy rules, to be filtered and evaluated based on constraints on the input.
It is further an objective of the present invention to combine this constraint to correspond to a concept or principle to deliver conceptual, qualitative feedback.
It is further an objective of the present invention to remind students of fundamental principles and their applications that should be learned as they attempt to understand problems. This occurs where a wrong step in a solution does not satisfy the constraint evaluated by the consistency rule.
It is further an objective of the present invention to say something educationally meaningful about a wrong answer, as a minimum, if a particular misconception is unidentified by the intelligent system.
It is yet another objective of the present invention to augment existing production rules with the functionalities of the consistency rules to increase the robustness of the intelligent tutorial.
It is further an objective of the present invention to allow for the diagnosis of multiple errors in a given single wrong step of a problem, and to display what each of those errors are.
Accordingly, what is provided is a computerized method for providing a meaningful response in an intelligent tutor, comprising the steps of accepting a problem and determining if this problem has a solution consistent with a plurality of applicable constraints. If the problem has a solution consistent with all applicable constraints, input in the form of a step to a solution is received having at least one of the constraints imposed thereon. It is then determined if the input violates a consistency rule, wherein at least one of the constraints is evaluated and compared to a fundamental rule set data structure containing a plurality of fundamental principles. Feedback can then be generated by telling the user the input is wrong because it violates at least one fundamental rule of the fundamental rule set.